Gauss–Legendre algorithm
The Gauss–Legendre algorithm is an algorithm to compute the digits of π. It is notable for being rapidly convergent, with only 25 iterations producing 45 million correct digits of π. However, it has some drawbacks (for example, it is computer memory-intensive) and therefore all record-breaking calculations for many years have used other methods, almost always the Chudnovsky algorithm. For details, see Chronology of computation of π.
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- enThe Gauss–Legendre algorithm is an algorithm to compute the digits of π. It is notable for being rapidly convergent, with only 25 iterations producing 45 million correct digits of π. However, it has some drawbacks (for example, it is computer memory-intensive) and therefore all record-breaking calculations for many years have used other methods, almost always the Chudnovsky algorithm. For details, see Chronology of computation of π.
- Has abstract
- enThe Gauss–Legendre algorithm is an algorithm to compute the digits of π. It is notable for being rapidly convergent, with only 25 iterations producing 45 million correct digits of π. However, it has some drawbacks (for example, it is computer memory-intensive) and therefore all record-breaking calculations for many years have used other methods, almost always the Chudnovsky algorithm. For details, see Chronology of computation of π. The method is based on the individual work of Carl Friedrich Gauss (1777–1855) and Adrien-Marie Legendre (1752–1833) combined with modern algorithms for multiplication and square roots. It repeatedly replaces two numbers by their arithmetic and geometric mean, in order to approximate their arithmetic-geometric mean. The version presented below is also known as the Gauss–Euler, Brent–Salamin (or Salamin–Brent) algorithm; it was independently discovered in 1975 by Richard Brent and Eugene Salamin. It was used to compute the first 206,158,430,000 decimal digits of π on September 18 to 20, 1999, and the results were checked with Borwein's algorithm.
- Hypernym
- Algorithm
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- Gauss–Legendre algorithm
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- enGauss–Legendre algorithm
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- Adrien-Marie Legendre
- Algorithm
- Arithmetic-geometric mean
- Arithmetic–geometric mean
- Arithmetic mean
- Borwein's algorithm
- Carl Friedrich Gauss
- Category:Pi algorithms
- Chronology of computation of π
- Chudnovsky algorithm
- Elliptic integral
- Eugene Salamin (mathematician)
- Geometric mean
- Iteration
- Numerical approximations of π
- Pi
- Quadratic convergence
- Random-access memory
- Richard Brent (scientist)
- Square root
- SameAs
- 2JiM7
- Algoritme van Gauss-Legendre
- Algoritmo de Gauss-Legendre
- Algoritmo de Gauss-Legendre
- Algoritmo di Gauss-Legendre
- Formule de Brent-Salamin
- Gauss-Legendre Algoritması
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- אלגוריתם גאוס-לז'נדר
- ガウス＝ルジャンドルのアルゴリズム
- 高斯-勒让德算法
- Subject
- Category:Pi algorithms
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- Gauss–Legendre algorithm?oldid=1115360431&ns=0
- WikiPageLength
- 6202
- Wikipage page ID
- 12916
- Wikipage revision ID
- 1115360431
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- Template:Pi
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